login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A075149 Sum_{i=0..2*A053645(n)} (C(2*A053645(n),i) mod 2)*A000045(n-i) [where C(r,c) is the binomial coefficient (A007318) and A000045(n) is the n-th Fibonacci number]. 2

%I #11 Jan 09 2024 12:08:21

%S 0,1,1,3,3,7,9,21,21,47,63,141,147,329,441,987,987,2207,2961,6621,

%T 6909,15449,20727,46347,46389,103729,139167,311187,324723,726103,

%U 974169,2178309,2178309,4870847,6534927,14612541,15248163,34095929,45744489

%N Sum_{i=0..2*A053645(n)} (C(2*A053645(n),i) mod 2)*A000045(n-i) [where C(r,c) is the binomial coefficient (A007318) and A000045(n) is the n-th Fibonacci number].

%H A. Karttunen, <a href="http://www.fq.math.ca/Papers1/42-1/quartkarttunen01_2004.pdf">On Pascal's Triangle Modulo 2 in Fibonacci Representation</a>, Fibonacci Quarterly, 42 (2004), 38-46.

%p with(combinat); [seq(A075149(n,n=0..50)]; A075149 := n -> add((binomial(2*r(n),i) mod 2)*fibonacci(n-i),i=0..2*r(n));

%p r := n -> n - 2^floor_log_2(n);

%p floor_log_2 := proc(n) local nn,i; nn := n; for i from -1 to n do if(0 = nn) then RETURN(i); fi; nn := floor(nn/2); od; end;

%Y Bisection gives A050614.

%K nonn

%O 0,4

%A _Antti Karttunen_, Sep 05 2002

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 07:18 EDT 2024. Contains 371235 sequences. (Running on oeis4.)